Abstract
We study systematic uncertainties in the lattice QCD computation of hadronic vacuum polarization (HVP) contribution to the muon $g-2$. We investigate three systematic effects; finite volume (FV) effect, cutoff effect, and integration scheme dependence. We evaluate the FV effect at the physical pion mass on two different volumes of (5.4 fm$)^4$ and (10.8 fm$)^4$ using the PACS10 configurations at the same cutoff scale. For the cutoff effect, we compare two types of lattice vector operators, which are local and conserved (point-splitting) currents, by varying the cutoff scale on a larger than (10 fm$)^4$ lattice at the physical point. For the integration scheme dependence, we compare the results between the coordinate- and momentum-space integration schemes at the physical point on a (10.8 fm$)^4$ lattice. Our result for the HVP contribution to the muon $g-2$ is given by $a_\mu^{\rm hvp} = 737(9)(^{+13}_{-18})\times 10^{-10}$ in the continuum limit, where the first error is statistical and the second one is systematic.
Highlights
The muon anomalous magnetic moment ðg − 2Þμ has been a key observable for a proof of predictability of quantum field theory
After subtracting these lattice artifacts [25,26,27], ΠðQ2Þ computed with Lattice QCD (LQCD) is consistent with the perturbative representation of the Adler function [28] in high Q2 > 1 GeV2 except for the nonperturbative objects such as the d-dimensional operator condensate term given by hOdi=Q2d appearing in the operator product expansion (OPE) [29]
III, we perform a systematic study of uncertainties stemming from the finite volume (FV) effect, the cutoff effect, and the integration scheme dependence in the LQCD calculation of ahμvp
Summary
The muon anomalous magnetic moment ðg − 2Þμ has been a key observable for a proof of predictability of quantum field theory. [17], the leading-order ChPT estimate is added to the lattice result on a ð5.4 fmÞ3 box at the physical pion mass taking higher-order contributions of Oðp4Þ as a systematic error. Reference [16] employs a similar strategy to add the ChPT estimate to the lattice results on ð6.1 − 6.6 fmÞ3 lattices around the physical pion mass but takes the systematic error conservatively. As pointed out in our previous study [22], it is essentially important to assess the FV effect in the LQCD calculation of ahμvp by employing the direct comparison between different volumes at the physical pion mass without any reliance on the effective models. We perform a more precise comparison with ChPT using a lattice larger than ð10 fmÞ4 at the physical pion mass, which are a subset of the PACS10 configurations [23].
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